Despite her initial screw-up – giving the love potion to Tristan and Yseut by mistake – Brangain is a devoted and loyal servant to Yseut throughout the story. Even when Yseut tries to have her killed, Brangain refuses to reveal Tristan and Yseut's affair. She also agrees to take Yseut's place in Mark's bed on their wedding night so that Mark will not discover his bride's lost virginity. We're surprised she didn't notice his horse's ears, but hey, it was dark.
Like her mistress, Brangain is clever, arranging secret meetings for Tristan and Yseut when they can no longer meet openly and seeing past Tristan's disguise as a fool long before Yseut does. Brangain's role as go-between moves the plot along; her substitute of her virginal body for Yseut's reveals the extent to which medieval marriage depends upon the disposability of women's bodies by those in power.
In this case, "those in power" includes Yseut, who orders the substitution in the first place and then decides she might as well lop off some inconvenient heads, too. We might ask how much agency these women have, and whether they have their own power structure that mirrors and interacts with the men's.